About the only reason I can see coring beams is for concrete strength in high shear areas... for normal reinforcing percentages, strength has little impact on flexural strength. If high shear is the issue, then an area of low shear, neutral axis is OK.
Before you core, you should have a procedure in the event of 'failure' already laid out.
coring was required since the structure is under structural investigation. the end user wants to know if retrofitting would be necessary or is the building members are adequate. part of the Terms of Reference is to conduct core test to determine the compressive strength of concrete and compare it with the general notes.
If absolutely necessary though, as for where, I would try to position the core in an area of low shear, and centered slightly below the neutral axis of the beam in an area of reduced moment, comparable to the section removed above the neutral axis if there is no shoring. I would definitely ferroscan the beam to find the reinforcing prior to coring so as little as possible is cut - hopefully none.
All this depends too on the size of the core in relation to the depth of the beam. I also assume that the core would be horizontally taken, not vertically.
Remember too, that one core will not guarantee you that the concrete is the same throughout the whole beam. It could take multiple cores to develop a degree of reliability here.
